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Supporting Information for ‘Electronic Structure of Hemin in Solution Studied by Resonant X-ray Emission Spectroscopy and Electronic Structure Calculations’ Kaan Ataka,b, Ronny Golnaka,c, Jie Xiaoa, Edlira Suljotia, Mika Pflügera, Tim Brandenburga, Bernd Wintera, Emad F. Aziz*,a,b a
Joint Laboratory for Ultrafast Dynamics in Solutions and at Interfaces (JULiq) Helmholtz-
Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany b
Freie Universität Berlin, Fachbereich Physik, Arnimallee 14, D-14195 Berlin, Germany
c
Freie Universität Berlin, Fachbereich Chemie, Takustr. 3, D-14195 Berlin, Germany
*
Corresponding Author
Email: [email protected]
1
Computational details During the optimization of the molecular geometries and the subsequent application of DFT/ROCIS for obtaining the XA spectra, we used the spin-unrestricted Kohn-Sham (UKS) method available in the ORCA software due to the open-shell nature of the TM complex under investigation. This leads to a good agreement with the experiment. Yet our interpretation suffers from the unrestricted nature of the method; the orbitals are split into two sets with α and β spin wavefunctions, with no restriction on the spatial part of the orbitals. This does not present a theoretical problem as individual MOs are not observables, but the spectra are. On the other hand, to be able to interpret the orbitals in the sense of bonding structure or energy levels, the use of one orbital set is more convenient, and can be provided by applying a restricted open-shell Kohn-Sham (ROKS) method. ORCA itself creates a similar set of orbitals called the quasirestricted orbital set for the DFT/ROCIS part, but ROKS can provide human readable orbital visualizations and population analyses in a straightforward fashion. However, ROKS calculations are more difficult to perform, during which self-consistent-field (SCF) convergence becomes problematic. Therefore, we calculated the spectra for different spin states and conformations using UKS method, and selected the best matching spectrum to the experimental result. We then repeated the XAS calculation for that particular case with ROKS method, and verified the spectrum to be essentially the same. The orbital energies presented by ROKS and the quasi restricted orbital method by DFT/ROCIS are found to be very similar. Unfortunately both of the methods suffer from the same well-known drawback: the violation of the Aufbau principle in determining the energies of the SOMOs.1–3 Therefore, when presenting the MO energies in
2
Table 1, it should be kept in mind that, the relative energies between these orbitals should be considered more physical than the absolute values.
FePPIXCl S=2.5
FePPIXCl S=1.5
FePPIXCl S=0.5
Fe-Cl bond distance (Å)
2.239
2.292
2.236
Fe-N bond distance (Å)
2.101, 2.107, 2.094, 2.103
2.025, 2.032, 2.016, 2.025
2.005, 2.016, 2.010, 2.012
Cl-Fe-N bond angle (⁰)
106.0, 105.5, 103.0, 103.1
100.2, 100.3, 97.8, 97.9
97.5, 100.8, 94.6, 96.9
N-Fe-N bond angle (⁰)
86.4, 86.7, 86.1, 86.6
88.5, 88.8, 88.3, 88.8
89.0, 89.4, 88.3, 89.6
4.14
4.85
3.92
-96826.98
-96826.90
-96826.38
Total dipole moment (Debye) Total single point energy (eV)
Table SI-1. The coordination of iron in FePPIX chloride varying with different spin configurations according to the B3LYP/def2-TZVP(-f)/def2-TZV/J unrestricted open shell DFT optimization calculations.
FePPIX S=2.5
FePPIX S=1.5
FePPIX S=0.5
Fe-N bond distance (Å)
2.062, 2.056, 2.059, 2.055
1.977, 1.973, 1.974, 1.970
1.994, 1.999, 1.990, 1.993
N-Fe-N bond angle (⁰)
90.0, 90.2, 89.5, 90.3
90.1, 90.2, 89.6, 90.3
89.9, 90.3, 89.7, 90.2
7.39
6.98
7.05
-84298.21
-84298.59
-84297.96
Total dipole moment (Debye) Total single point energy (eV)
Table SI-2. The coordination of iron in FePPIX varying with different spin configurations according to the B3LYP/def2-TZVP(-f)/def2-TZV/J unrestricted open shell DFT optimization calculations.
3
Figure SI-1. Experimental iron L-edge PFY spectrum of 50mM FePPIX chloride solution in DMSO and DFT/ROCIS XA calculations for spin multiplicity 6 with the presence and absence of spin-orbit coupling effect. (a), (b), and (c) refer to pre-maximal, maximal and post-maximal features respectively.
4
Figure SI-2. Inner valence molecular orbitals of FePPIX chloride (in high spin configuration, S=2.5) with prominent iron contribution (refer to Table 1) according to the B3LYP/def2-TZVP(f)/def2-TZV/J restricted open shell single point DFT calculation.
References (1) Plakhutin, B. N.; Davidson, E. R. Koopmans’ Theorem in the Restricted Open-Shell Hartree−Fock Method. 1. A Variational Approach†. J. Phys. Chem. A 2009, 113, 12386– 12395. (2) Plakhutin, B. N.; Davidson, E. R. Canonical Form of the Hartree-Fock Orbitals in OpenShell Systems. J. Chem. Phys. 2014, 140, 014102. (3) Jensen, F. Introduction to Computational Chemistry; John Wiley & Sons: Chichester, England; Hoboken, NJ, 2007.
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Joint Laboratory for Ultrafast Dynamics in Solutions and at Interfaces (JULiq) Helmholtz-
Zentrum Berlin für Materialien und Energie, Albert-Einstein-Strasse 15, 12489 Berlin, Germany b
Freie Universität Berlin, Fachbereich Physik, Arnimallee 14, D-14195 Berlin, Germany
c
Freie Universität Berlin, Fachbereich Chemie, Takustr. 3, D-14195 Berlin, Germany
*
Corresponding Author
Email: [email protected]
1
Computational details During the optimization of the molecular geometries and the subsequent application of DFT/ROCIS for obtaining the XA spectra, we used the spin-unrestricted Kohn-Sham (UKS) method available in the ORCA software due to the open-shell nature of the TM complex under investigation. This leads to a good agreement with the experiment. Yet our interpretation suffers from the unrestricted nature of the method; the orbitals are split into two sets with α and β spin wavefunctions, with no restriction on the spatial part of the orbitals. This does not present a theoretical problem as individual MOs are not observables, but the spectra are. On the other hand, to be able to interpret the orbitals in the sense of bonding structure or energy levels, the use of one orbital set is more convenient, and can be provided by applying a restricted open-shell Kohn-Sham (ROKS) method. ORCA itself creates a similar set of orbitals called the quasirestricted orbital set for the DFT/ROCIS part, but ROKS can provide human readable orbital visualizations and population analyses in a straightforward fashion. However, ROKS calculations are more difficult to perform, during which self-consistent-field (SCF) convergence becomes problematic. Therefore, we calculated the spectra for different spin states and conformations using UKS method, and selected the best matching spectrum to the experimental result. We then repeated the XAS calculation for that particular case with ROKS method, and verified the spectrum to be essentially the same. The orbital energies presented by ROKS and the quasi restricted orbital method by DFT/ROCIS are found to be very similar. Unfortunately both of the methods suffer from the same well-known drawback: the violation of the Aufbau principle in determining the energies of the SOMOs.1–3 Therefore, when presenting the MO energies in
2
Table 1, it should be kept in mind that, the relative energies between these orbitals should be considered more physical than the absolute values.
FePPIXCl S=2.5
FePPIXCl S=1.5
FePPIXCl S=0.5
Fe-Cl bond distance (Å)
2.239
2.292
2.236
Fe-N bond distance (Å)
2.101, 2.107, 2.094, 2.103
2.025, 2.032, 2.016, 2.025
2.005, 2.016, 2.010, 2.012
Cl-Fe-N bond angle (⁰)
106.0, 105.5, 103.0, 103.1
100.2, 100.3, 97.8, 97.9
97.5, 100.8, 94.6, 96.9
N-Fe-N bond angle (⁰)
86.4, 86.7, 86.1, 86.6
88.5, 88.8, 88.3, 88.8
89.0, 89.4, 88.3, 89.6
4.14
4.85
3.92
-96826.98
-96826.90
-96826.38
Total dipole moment (Debye) Total single point energy (eV)
Table SI-1. The coordination of iron in FePPIX chloride varying with different spin configurations according to the B3LYP/def2-TZVP(-f)/def2-TZV/J unrestricted open shell DFT optimization calculations.
FePPIX S=2.5
FePPIX S=1.5
FePPIX S=0.5
Fe-N bond distance (Å)
2.062, 2.056, 2.059, 2.055
1.977, 1.973, 1.974, 1.970
1.994, 1.999, 1.990, 1.993
N-Fe-N bond angle (⁰)
90.0, 90.2, 89.5, 90.3
90.1, 90.2, 89.6, 90.3
89.9, 90.3, 89.7, 90.2
7.39
6.98
7.05
-84298.21
-84298.59
-84297.96
Total dipole moment (Debye) Total single point energy (eV)
Table SI-2. The coordination of iron in FePPIX varying with different spin configurations according to the B3LYP/def2-TZVP(-f)/def2-TZV/J unrestricted open shell DFT optimization calculations.
3
Figure SI-1. Experimental iron L-edge PFY spectrum of 50mM FePPIX chloride solution in DMSO and DFT/ROCIS XA calculations for spin multiplicity 6 with the presence and absence of spin-orbit coupling effect. (a), (b), and (c) refer to pre-maximal, maximal and post-maximal features respectively.
4
Figure SI-2. Inner valence molecular orbitals of FePPIX chloride (in high spin configuration, S=2.5) with prominent iron contribution (refer to Table 1) according to the B3LYP/def2-TZVP(f)/def2-TZV/J restricted open shell single point DFT calculation.
References (1) Plakhutin, B. N.; Davidson, E. R. Koopmans’ Theorem in the Restricted Open-Shell Hartree−Fock Method. 1. A Variational Approach†. J. Phys. Chem. A 2009, 113, 12386– 12395. (2) Plakhutin, B. N.; Davidson, E. R. Canonical Form of the Hartree-Fock Orbitals in OpenShell Systems. J. Chem. Phys. 2014, 140, 014102. (3) Jensen, F. Introduction to Computational Chemistry; John Wiley & Sons: Chichester, England; Hoboken, NJ, 2007.
5
